Optimal. Leaf size=19 \[ \log \left (\left (3 x+\frac {3}{5} \log (5) \log \left (-\frac {x}{5}\right )\right )^2\right ) \]
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Rubi [A]
time = 0.09, antiderivative size = 16, normalized size of antiderivative = 0.84, number of steps
used = 2, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {2641, 6816}
\begin {gather*} 2 \log \left (5 x+\log (5) \log \left (-\frac {x}{5}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2641
Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {10 x+2 \log (5)}{x \left (5 x+\log (5) \log \left (-\frac {x}{5}\right )\right )} \, dx\\ &=2 \log \left (5 x+\log (5) \log \left (-\frac {x}{5}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 17, normalized size = 0.89 \begin {gather*} 2 \log \left (-5 x-\log (5) \log \left (-\frac {x}{5}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 9.51, size = 15, normalized size = 0.79
method | result | size |
derivativedivides | \(2 \ln \left (\ln \left (5\right ) \ln \left (-\frac {x}{5}\right )+5 x \right )\) | \(15\) |
default | \(2 \ln \left (\ln \left (5\right ) \ln \left (-\frac {x}{5}\right )+5 x \right )\) | \(15\) |
norman | \(2 \ln \left (\ln \left (5\right ) \ln \left (-\frac {x}{5}\right )+5 x \right )\) | \(15\) |
risch | \(2 \ln \left (\ln \left (-\frac {x}{5}\right )+\frac {5 x}{\ln \left (5\right )}\right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 25, normalized size = 1.32 \begin {gather*} 2 \, \log \left (-\frac {\log \left (5\right )^{2} - \log \left (5\right ) \log \left (-x\right ) - 5 \, x}{\log \left (5\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 14, normalized size = 0.74 \begin {gather*} 2 \, \log \left (\log \left (5\right ) \log \left (-\frac {1}{5} \, x\right ) + 5 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 15, normalized size = 0.79 \begin {gather*} 2 \log {\left (\frac {5 x}{\log {\left (5 \right )}} + \log {\left (- \frac {x}{5} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 14, normalized size = 0.74 \begin {gather*} 2 \, \log \left (\log \left (5\right ) \log \left (-\frac {1}{5} \, x\right ) + 5 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.75, size = 13, normalized size = 0.68 \begin {gather*} 2\,\ln \left (x+\frac {\ln \left (-\frac {x}{5}\right )\,\ln \left (5\right )}{5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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